Alfred Still.

Principles of electrical design; d. c. and a. c. generators online

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judgment and developing ingenuity or inventiveness; but it
will at least help to bridge the gap between the purely academic
and logically argued teachings of the schools, and the methods of
the practical engineer, who requires results of commercial value
quickly, with sufficient, but not necessarily great, accuracy, and
who usually depends more upon his intuition and his quickness
of perception, than upon any logical method of reasoning.

It must not be thought that these remarks tend to belittle or
underrate the method of obtaining results through a sequence of
logically proven steps; on the contrary, this is the only safe
method by which the accuracy of results can be checked, and it is
the method which is followed, whenever possible, throughout
this book. It is not by the reading of any book that the art of
designing can be learned; but only by applying the information
gathered from such reading to the diligent working out of
numerical examples and problems.

Although the work done in the drafting room is not necessarily
designing, it does not follow that the designer need know nothing
about engineering drawing. The art of making neat sketches
or clear and accurate drawings of the various parts of a machine,
is learnt only by practice; yet every engineer, whatever line of
work he may follow, should be able not only to understand and
read engineering drawings, but to produce them himself at need.
It is particularly important that he should be able to make neat
dimensioned sketches of machine parts, because, in addition to
the practical value of this accomplishment, it is an indication
that he has a clear conception of the actual or imagined thing,
and can make his ideas intelligible to others. Clear thinking is
absolutely essential to the designer. He must be able to visualize
ideas in his own mind before he can impart these ideas to others.
Young men seldom realize the importance of learning to think,
neither do they know how few of their elders ever exercise their
reasoning faculty. The man who can always express himself
clearly, either in words or by sketches and drawings, is invariably
one whose thoughts are limpid and who can therefore realize a
clear mental picture of the thing he describes. The ability to


"see things" in the mind is an attribute of every great engineer.
Vagueness of thought and mental inefficiency are revealed by
untidy and inaccurate sketches, poor composition and illegible
writing. It is, however, possible to train the mind and greatly
increase its efficiency by developing neatness and accuracy in
the making of sketches, and by the study of languages.

The knowledge of foreign languages has an obvious practical
value apart from its purely educational advantage, but the study
of English, for the engineer of English-speaking countries, is of
far greater importance. By enlarging and enriching one's
vocabulary through the reading of high class literature, and by
paying constant attention to the correct meaning of words and
their proper connection in spoken and written language, the
clearness of thought important to every engineer, and essential
to the designer, may be cultivated to an extent which the average
student in the technical schools and engineering universities
entirely fails to recognize. In an address delivered on April 8,
1904, to the Engineering Society of the University of Nebraska,
DR. J. A. L. WADDELL said,

"Too much stress cannot well be laid on the importance of a thorough
study of the English language. Given two classmate graduates of equal
ability, energy, and other attributes contributary to a successful career,
one of them being in every respect a master of the English language
and the other having the average proficiency in it, the former is certain to
outstrip the latter materially in the race for professional advancement."

Considering further the difference between the training re-
ceived by the student in the schools and the training he will
subsequently receive in the world of practical things, it must
be remembered that the object of technical education is mainly
to develop the mind as a thinking machine, and provide a good
working basis of fundamental knowledge which shall give weight
and balance to all future thinking. The commercial aspect of
engineering is seen more clearly after leaving school because it
is not easily taught in the class room. The student does not,
therefore, get a proper idea of the value of time. Engineering
is the economical application of science to material ends, and if
the items of cost and durability are omitted from a problem, the
results obtained however important from other points of view
have no engineering value. The cost of all finished work,
including that of the raw materials used in construction, is the


cost of labor. Provided the work is carefully done, the element
of time becomes, therefore, of the greatest importance. A
student in a technical school may be able to produce a neat and
correct drawing, but the salary he could earn as a draughtsman
in an engineering business might be very small because his rate
of working will be slow. The designer must always have in
mind the question of cost, not only material cost which is
fairly easy to estimate but also labor cost, which depends on
the size and complication of parts, accessibility of screws and
bolts, and similar factors. These things are rarely learned
thoroughly except by actual practice in engineering works, but
the student should try to realize their importance, and bear
them in mind. A study of design will do something toward
teaching a man the value of his time. Thus, although it is
important to check and countercheck all calculations, and time
so spent is rarely wasted, yet it is essential to know what degree
of approximation is allowable in the result. This is a matter of
judgment, or a sense of the absolute and relative importance of
things, which is developed only with practice. What is worth
doing, what is expedient, and what would be mere waste of time,
may be learned surely, if slowly, by the study and practice of
machine design.

It is by taking on responsibilities that confidence and self-
reliance are developed; and the student may work out examples
in design by following his own methods, regardless of the par-
ticular practice advocated by a book or teacher. He can usually
check his results and satisfy himself that they are substantially
correct. This will give him far more encouragement and
satisfaction than the blind application of proven rules and for-
mulas. By making mistakes that are frequently due to
oversights or omissions and by having to go over the ground a
second or third time in order to rectify them, an important
lesson is learned, namely, that one must resist the tendency to
jump at conclusions. The necessity of checking one's work,
and proceeding systematically by doing at the right time and in
the right place the particular thing that should be done before
all others, is of great value in developing one of the most im-
portant qualifications of the engineer. This has already vaguely
be^n referred to as engineering judgment, a sense of proportion,
seeing the fitness of things; but all these are allied, if not actually
identical, with the one faculty of inestimable value known as


common sense, so called according to the definition of a witty
Frenchman because it is the least common of the senses.

It should be realized clearly that the true designer is a maker,
not an imitator. The function of the designer is to create. His
value as a live factor in the engineering world will increase by
just so much as he rises above the level of the mere copyist.
The man who can see what has to be done, and how it may be
done, is always of greater value than the man who merely does a
thing, however skilfully, when the manner of doing it has been
explained to him.

In addition to a sound knowledge of engineering principles
and practice, a designer should preferably have a leaning toward
original investigation or research work. He should not be bound
by the trammels of convention, nor discouraged by the ground-
less belief that what has been done before has necessarily been done
rightly. On the contrary, he should assert his personality, and
have the courage of his own opinions, provided these are based,
and intelligently formed, on established fundamental principles,
the truth and soundness of which are undeniable.

If the chief function of the designing engineer is to create,
the cultivation of the imagination is obviously of the utmost
value. This is a point that is frequently overlooked. In other
creative arts, such as poetry and painting, intuition and a fertile
imagination are considered essential to success, and there can be
ho' valid reason for undervaluing the possession of these qualities
by the engineer. The work of the designer is artistic rather
than purely scientific; that is to say it requires skill and ingenuity
in addition to mere knowledge. Without a sound basis of
engineering knowledge, the designer is not likely to succeed,
because his conceptions, like those of many so-called inventors,
would have no practical application; but it is also true that the
great designers, even of mechanical and electrical machinery, do
not always understand why they have done a certain thing in a
certain way. They work by intuition rather than by methods
that are obviously logical, but their early training and thorough
knowledge of engineering facts and practice act as a constant
and useful check, with the result that they rarely make mistakes
of serious importance.

It is not suggested that the exalted moods and "inspired
imaginings" of the poet or artist would be of material advantage


to the practical engineer; but the present writer wishes to state,
most emphatically, that, in his opinion, the average engineer
does not rate imagination at its proper value, neither does he
cultivate it as he might, did he realize the advantages if only
from a grossly commercial standpoint that would thereby
accrue. There is to-day a tendency to underestimate the
value of abstract speculation and the pursuit of any study
or enterprise of which the immediate practical end is not obvious.
The fact that the indirect benefit to be derived therefrom may,
and generally does, greatly outweigh the apparent advantages
of so-called utilitarian lines of study, is generally overlooked.
It is an admitted fact that the outlook of the graduate from
many of the engineering schools is narrow: this is no doubt
largely due to faults in the system and the teachers; but the
student himself is apt to neglect his opportunities for the study
of subjects such as general literature, languages, history, and
political economy, on the plea that he would be wasting his time.
It is only at a later period of his engineering career that he
begins to realize how an intelligent and appreciative study of
these broader subjects would have stimulated his mind and
cultivated his imagination to a degree which would be a great
and lasting benefit to him in his profession.

It is unfortunate that neither the nature of the subject nor the
manner in which it is presented in the following chapters is
likely to stimulate the imaginative faculty; but the writer be-
lieves that no apology is needed for referring in this chapter to
subjects outside the scope of the main portion of the book.
In presenting fundamental principles and showing how they may
be applied to the design of machines, it is necessary to arrange
the matter in accordance with some logical scheme; and it is
just because a book such as the present one cannot give, and
does not claim to give, all that goes to the making of a designing
engineer, that it was deemed advisable to say something of
a general nature relating to the art of designing electrical

The principles underlying the action of dynamo-electric
machinery may be studied under two main headings:

1. The magnetic condition due to an electric current in a
conductor or exciting coil.

2. The e.m.f. developed in a conductor due to changes in
the magnetic condition of the surrounding medium.


This last effect, which may be attributed to the cutting of the
magnetic lines by the electric conductors, will be considered
when taking up the design of dynamos. For the present it will
be advisable to investigate condition (1) only, and Chaps.
II and III will be devoted to the study of the magnetic circuit;
to the calculation of the excitation required to produce a given
magnetic flux; or, alternatively, the quantitative determination
of the flux when the size, shape, and position, of the exciting
coils are known.


In all dynamo-electric machinery, coils of wire carrying electric
currents produce a magnetic field in the surrounding medium
whether air or iron and the purport of this chapter is to show
how the magnetic condition due to an electric current can be
determined within a degree of accuracy generally sufficient for
practical purposes.

The design of the magnetic circuit of dynamo-electric genera-
tors does not differ appreciably from the design of electromagnets
for lifting or other purposes, and it is, therefore, proposed to
consider, in the first place, the fundamental principles and
calculations involved in proportioning and winding electro-
magnets to fulfil specified requirements. Particular attention
will be paid to types of magnets with small air gaps because these
serve to illustrate the conditions met with in field-magnet design,
and the principles of the magnetic circuit can be applied with
but little difficulty; while, in the case of coreless solenoids or
magnets with very large air gaps, the p&ths of the magnetic flux
cannot readily be predetermined, and empirical formulas or
approximate methods of calculation have to be used. When the
magnetic circuit is mainly through iron, and the air gaps are
comparatively short, it is generally possible to picture the lines
or tubes of magnetic flux linking with the electric circuit, thus
facilitating the quantitative calculation of the flux at various
parts in the circuit; but when the path of the magnetic lines
is largely through air or other "non-magnetic" material, the
analogy between the magnetic and electric circuits is less con-
venient and may indeed lead to confusion; the quantitative
calculations become more difficult and less scientific, calling for
an experienced designer if results of practical value are desired.

1. The Magnetic Circuit. Without dwelling on the mathe-
matical conceptions of the physicist, which may be studied in
all books on magnetism, it may be stated without hesitation
that the analogy between the magnetic and electric circuits,
and the idea of a closed magnetic circuit linked with every electric



circuit, will be most useful to the designer of electrical machinery.
The magnetic flux is thought of as consisting of a large number of
tubes of induction, each tube being closed upon itself and linked
with the electric circuit to which the magnetic condition is
due. The distribution of the magnetic field will depend upon the
shape of the exciting coils, and upon the quality, shape, and
position, of the iron in the magnetic circuit. The amount of
the magnetic flux in a given magnetic circuit will depend upon
the m.m.f. (magnetomotive force) and therefore on the current
and number of turns of wire in the exciting coils.

OHM'S law for the electric circuit can be put in the two forms:

e.m.f. T E

(a) Current = r , or / =

resistance R

(6) Current = e.m.f. X conductance, or I = E X ( B)

Similarly, in the magnetic circuit:

magnetomotive force
(a) Magnetic flux of induction = -

magnetic reluctance


* - ^t (1)

(6) Magnetic flux = magnetomotive force X permeance
or <*> = m.m.f. X P (2)

In this analogy, 4> is the total flux of induction, usually ex-
pressed in C.G.S. lines, or maxwells; m.m.f. is the force tending
to produce the magnetic condition expressed in ampere-turns
(Jjte engineer's unit) or in gilberts the C.G.S. unit; and reluctance
is the magnetic equivalent of resistance in the electric circuit.
It is necessary to bear in mind that although these are funda-
mental formulas of the greatest value in the calculation of mag-
netic circuits, yet they are based on an analogy which, with
all its advantages, has its limitations. The chief difference
between OHM'S law of the electric circuit and the analogous
expression as applied to the magnetic circuit lies in the fact that
the magnetic reluctance does not depend merely upon the
material, length, and cross-section, of the various parts of the
magnetic circuit, but also when iron is present on the amount
of the flux, or, more properly, on the flux density, which is an
important factor in the determination of the permeability (/*).


2. Definitions. Magnetomotive Force. The difference of mag-
netic potential which tends to set up a flux of magnetic induction
between two points is called the magnetomotive force (m.m.f.)
between those points. The unit m.m.f. known as the gilbert
will set up unit flux of induction between the opposite faces of
a centimeter cube of air. If we consider any closed tube of
induction linked with a coil of S turns carrying a current of
/ amperes, the total ampere turns producing this induction are
SI, and the total m.m.f. is,

m.m.f. = JQ SI gilberts. 1

Magnetizing Force. The magnetomotive force per centimeter
is called the magnetizing force, or magnetic force. The symbol H
is generally used to denote this quantity which is also referred to
as the intensity of the magnetic field, or simply field intensity,
at the point considered. The magnetomotive force is, therefore,
the line integral of the magnetizing force, or,

m.m.f. = 2#SZ

where dl is a short portion of the magnetic circuit expressed in
centimeters over which the magnetizing force H is considered of
constant value. Thus H = QAir X ampere-turns per centimeter

= 0.47T-7- or, if it is preferred to use ampere-turns per inch

(not uncommon in engineering work), we may write H = 0.495
(SI per inch) .

1 What the practical designer wants to know is the number of ampere-


turns required to produce a given magnetic flux. The factor y^ constantly

enters into magnetic calculations as it is required to convert the engineer's
unit (ampere-turn) into the C.G.S. unit (gilbert). It should not be neces-
sary to explain its presence here, because this is done more or less lucidly in
most textbooks of physics. It should be sufficient to remind the reader
that the introduction of this factor is due to the physicist's conception of
the unit magnetic pole which he has endued with the ability to repel a
similar imaginary pole with a force of 1 dyne when the distance between
the two unit poles is 1 cm. Now, since, at every point on the surface of a
sphere of 1 cm. radius surrounding a unit magnetic pole placed at the center,
a similar pole will be repelled with a force of 1 dyne, there must be unit flux
density over this surface; that is to say, a flux of 1 maxwell per square centi-
meter. The surface of the sphere being 4?r sq. cm., it follows that 4ir lines
of flux must be thought of as proceeding from every pole of unit strength.
The factor 10 in the denominator converts amperes into absolute C.G.S.
units of current.


Magnetic Flux. The unit of magnetic flux is the maxwell;
it should be considered as a tube of induction having an ap-
preciable cross-section which may vary from point to point. The
expression " magnetic lines/' which is customary and convenient,
should suggest the center lines of these small unit tubes of in-
duction. The total number of unit magnetic lines through a
given cross-section will be denoted by the symbol <I>.

Flux, Density. The unit of flux density is the gauss; it is a
density of 1 maxwell per centimeter of cross-section. Thus, if
A is the cross-section, in square centimeters, of a magnetic
circuit carrying a total flux of & maxwells uniformly distributed
over the section, the flux density is B = <J> /A gausses. The
symbol B will be used throughout to denote gausses.

Permeability. What may be thought of as the magnetic
conductivity of a substance is known as permeability and rep-
resented by the symbol M- Unlike electrical conductivity, it
is not merely a physical property of the substance, because
in the case of iron, nickel, and cobalt it depends also upon the
flux density. For practical purposes, the permeability of all
substances, excepting only iron, nickel, and cobalt, is taken as
unity. Permeability can, therefore, be defined as the ratio of
the magnetic conductivity of a substance to the magnetic con-
ductivity of air.

Reluctance and Permeance. Magnetic permeanace is the re-
ciprocal of reluctance; a knowledge of the permeance of the
various paths is useful when considering magnetic circuits in
parallel, while reluctance is more convenient to use when making
calculations on magnetic paths in series. The reluctance of a
path of unit permeability is directly proportional to its length
and inversely proportional to its cross-section. Thus,

Reluctance of magnetic path in air = -r


Reluctance of magnetic path in iron = j


If the dimensions are in centimeters, the reluctance will be
expressed in oersteds.

1 /iA

Permeance = \

reluctance I

When calculating reluctance or permeance for use in the fun-
damental formulas (1) or (2) it is important to express all


dimensions in centimeters; no constants have then to be in-
troduced because, with the C.G.S. system of units,

m.m.f. in gilberts

Flux in maxwells

reluctance in oersteds

The sketch, Fig. 1, shows a (closed) tube of induction linked
with a coil of wire of S turns through which a current of / amperes
is supposed to be passing. This tube of induction consists of a
number of unit tubes or so-called magnetic lines each of which is
closed on itself. It follows that the total flux 3> is the same
through all cross-sections of the magnetic tube of flux indicated

FIG. 1. Tube of induction linked with coil.

in Fig. 1. The cross-section may, and generally does, vary from
point to point of the magnetic circuit, and since the total flux
$ is of constant value, the density B will be inversely proportional
to the cross-section. Thus, at a given point where the cross-
section is A i square centimeters the density in gausses is BI =

Turning again to the fundamental formula of the magnetic
circuit, we have,

m.m.f. = flux X reluctance

gilberts = maxwells X oersteds

0.4x37 = $ X (-7^- + -A- + etc.) (3)

Vd* ^-2M2 /

Also, since m.m.f. = magnetizing force X length of path, it is
sometimes convenient to put the above general expression in
the form

QAirSI = HJi + H 2 1 2 + etc. (4)


3. Effect of Iron in the Magnetic Circuit. Consider a toroid
or closed anchor-ring of iron of uniform cross-section A square
centimeters, wound with SI ampere-turns evenly distributed.

Applying the fundamental formula <f> = m.m.f. X P, we have,

$ = OAirSI X ^y

in which I is the average length of the magnetic lines, or irD
centimeters, where D is the average diameter of the ring.

Thus, if fj, is known, the flux in the ring can be calculated for
any given value of the exciting ampere-turns *S7. Since /* is a
function of the density B, and B = $/A it may be convenient to
put the above expression in the form

B =

Also, since m.m.f. (in gilberts) = HI

B = HI X |


whence n = ' which explains why the permeability is sometimes

referred to as the multiplying power of the iron. Thus, for a
given value of H, the magnetic flux in air will be H lines per
square centimeter of cross-section, but if the air is replaced by
iron, it will be pH or B lines. This accounts for the fact that
H (the magnetizing force, or m.m.f. per centimeter) is also
referred to as the intensity of the magnetic field, or magnetizing
intensity, and, as such, expressed in gausses. This conception
is liable to lead to confusion of ideas; but it is well to bear in
mind that, in air and other "non-magnetic" materials, the
numerical value of B is the same as that of H.

For a given magnetizing force H (or exciting ampere-turns per
